Home Work #7

Due Date:29 April, 2010

(Turn in your assignment at the mail box of S581 outside the ME general

office)

The solutions must be written on single-side A4 papers only.

HW 7-Problem #1A bar of rectangular cross section is loaded and supported as shown in the figure. The distance between supports is L= 1.2 m and the height of the bar is h=100 mm. The deflection δ at the midpoint is measured as 3.6 mm.

What is the maximum normal strain at the top and bottom of the bar?

HW 7-Problem #2A freight-car axle AB is loaded approximately as shown in the figure, with the forces P representing the car loads (transmitted to the axle through the axle boxes) and the forces R representing the rail loads (transmitted to the axle through the wheels). The diameter of the axle is d=80 mm, the distance between centers of the rails is L, and the distance between the forces P and R is b=200 mm.

Calculate the maximum bending stress σmax in the axle if P=47 KN.

HW 7-Problem #3

Determine the maximum tensile tress σt (due to pure bending by positive bending moments M) for beams having cross sections as follows:(a) A semicircle of diameter d, and (b) an isosceles trapezoid with bases b1=b and b2=4b/3, and altitude h.

HW 7-Problem #4A horizontal shelf AD of length L=900 mm, width b=300 mm, and thickness t=20 mm is supported by brackets at B and C (figure a). The brackets are adjustable and may be placed in any desired positions between the ends of the shelf. A uniform load of intensity q, which includes the weight of the shelf itself, acts in the shelf (figure b).Determine the maximum permissible value of the load q if the allowable bending stress in the shelf is σallow=5.0 MPa and the position of the support is adjusted for maximum load-carrying capacity.